#### Title

An Introduction to (1,2) - Domination Graphs

#### Document Type

Article

#### Language

eng

#### Format of Original

6 p.

#### Publication Date

2011

#### Publisher

Utilitas Mathematica Publishing Inc.

#### Source Publication

Congressus Numerantium

#### Source ISSN

0384-9864

#### Abstract

Using the graph definition of secondary domination by S. T. Hedetniemi et al., we extend the concept to digraphs. Here, we define a (1,2)-domination graph of a digraph D, dom 1,2 (D). Given vertices x and y in a digraph D, x and y form a (1,2)-dominating pair if and only if for every other vertex z in D, z is one step away from x or y and at most two steps away from the other. The (1,2)-dominating graph of a digraph D is defined to be the graph G=(V,E), where V(G)=V(D), and xy is an edge of G whenever x and y are a (1,2)-dominating pair in D. In this paper, we restrict our results to those involving tournaments. We show instances where dom 1,2 (D)=dom(D), and where the two graphs are quite different. An algorithm is given for embedding any domination graph of a tournament into the (1,2)-domination graph of a tournament.

#### Recommended Citation

Factor, Kim A. S. and Langley, Larry J., "An Introduction to (1,2) - Domination Graphs" (2011). *Mathematics, Statistics and Computer Science Faculty Research and Publications*. 377.

https://epublications.marquette.edu/mscs_fac/377

## Comments

Congressus Numerantium, No. 199 (2011): 33-38.